<p>Mesoscale eddies play a pivotal role in deciphering the intricacies of ocean dynamics and the transport of heat, salt, and nutrients. Accurate representation of these eddies in ocean models is essential for improving model predictions. In this study, we propose a convolutional neural network (CNN) that combines data-driven techniques with physical principles to develop a robust and interpretable parameterization scheme for mesoscale eddies in ocean modeling. We use a high-resolution reanalysis dataset to extract subgrid eddy momentum and then applying machine learning algorithms to identify patterns and correlations. To ensure physical consistency, we have introduced conservation of momentum constraints in our CNN parameterization scheme through soft and hard constraints. The interpretability analysis illustrate that the pre-trained CNN parameterization shows promising results in accurately solving the resolved mean velocity and effectively capturing the representation of unresolved subgrid turbulence processes. Furthermore, to validate the CNN parameterization scheme offline, we conduct simulations using the Massachusetts Institute of Technology general circulation model (MITgcm) ocean model. A series of experiments is conducted to compare the performance of the model with the CNN parameterization scheme and high-resolution simulations. The offline validation demonstrates the effectiveness of the CNN parameterization scheme in improving the representation of mesoscale eddies in the MITgcm ocean model. Incorporating the CNN parameterization scheme leads to better agreement with high-resolution simulations and a more accurate representation of the kinetic energy spectra.</p>